RNC Chairman Reince Priebus fought back this week after MSNBC's Twitter account said of a Cheerios ad featuring a biracial family: "Maybe the rightwing will hate it, but everyone else will go awww: the adorable new #Cheerios ad w/ biracial family.''

Priebus said RNC staff members would stay off the network until there was an apology from MSNBC's president, which he later issued.

"There is no question the agenda that MSNBC has and we all get that. They are a left-wing news organization and that's fine. We live in a country that allows free speech and that's part of the thing and that's what they're allowed to do," Spicer said.

"But, over the course of the last several weeks, a lot of their hosts have used inflammatory kind of over-the-line language and the other night, their network itself, not just a host, the network actually tweeted out [the] offensive tweet."

Spicer said the liberal media believes "it's acceptable to slap down conservatives because their ideas aren't good enough and no one seems to mind."

"What the RNC has been trying to do, whether it was the debates that CNN and NBC hosted, whether it was this instance, is to start inserting ourselves and standing up."